May 14, 2015 6:09 AM EDT

With the parliamentary elections behind us, we now have an unobstructed view of how one of the world’s most important political stories will unfold. Prime Minister David Cameron, who shocked pollsters by winning an outright majority in elections on May 7, promised voters a referendum by the end of 2017 on whether Britain will remain a member of the European Union. Some observers say that it’s all smoke, that Britons surely won’t vote to exit the E.U. Maybe. But the possibility of an exit–and the fear, anxiety and opportunism it generates–make this a story the world dare not ignore.

Britain’s economy is among the strongest in Europe. Its GDP grew by 2.6% last year, one of the best performances in the developed world. Employment stands at a record high. Yet Britain’s election results prove once again that the anti-E.U. populism now roiling European politics is alive and well in the U.K. Conservatives won their majority in part by promising a vote on E.U. membership that many party members don’t actually want. Labour, which carefully hedged its referendum bets, took a beating of surprising scale. The election’s biggest loser, the centrist Liberal Democrats, proved beyond a doubt that in this political climate, the middle of the road is the surest place to get hit by a truck.

The only pro-E.U. winner in Britain’s vote was the Scottish National Party (SNP), which won 56 of Scotland’s 59 contested seats just months after leading a failed effort to win Scotland’s independence from the U.K. Another winner was the Euroskeptic right-wing U.K. Independence Party (UKIP). The party won just one seat in the House of Commons, but its 12.6% of the national vote was more than either the Liberal Democrats or SNP could muster. Beyond its seat or vote count, UKIP has changed British politics by giving voice to public frustration with the E.U. and pushing the referendum to center stage.

Now the referendum is coming. What’s at stake? In many ways, E.U. membership has served Britain well–particularly its supersize banking sector, which has helped make London into a global city. In 2014, financial and insurance services brought in $193.7 billion in gross value added (GVA) to the U.K. economy, totaling 8% of the U.K.’s GVA. It’s little surprise, then, that fear of a British exit–which could seriously upset the international banking industry–has persuaded some U.K. financial institutions to send up warnings. Some 72% of British companies polled by the firm Grant Thornton say an exit would hurt business. HSBC has warned that it would consider relocating its headquarters from London should the U.K. leave the E.U.

No wonder British firms are on edge. By some estimates, “Brexit” would cost the U.K. $330 billion, or 14% of its GDP. After leaving, Britain would have to renegotiate trade relationships with individual E.U. members, and its government would lose much of its international clout. London would also become a less important ally for the U.S., which values Britain in part for its influence within the E.U. Finally, if polls suggest that a British exit is really possible, an empowered SNP might demand that overwhelmingly pro-E.U. Scots again get to vote on Scottish independence–and this time, they might well win.

The E.U. would also lose from a British exit, which would cost it 12.5% of its population, 14.8% of its economy and an experienced and engaged military power with the E.U.’s strongest ties to Washington. It’s also worth noting that Britain contributed more than $19 billion to the E.U. budget in 2013 while taking out just $7.1 billion. If Britain exits, Germany and others will have to make up the difference.

Right now, British voters are roughly split on an E.U. exit. In a recent poll by the consultancy Populus, 39% said they want to leave, while about 40% said they want to stay. That leaves a lot of undecided voters, and much will happen over the next two years. Bets will be hedged and preparations made, in Britain and across Europe. That alone will be a story worth following.

Foreign-affairs columnist Bremmer is the president of Eurasia Group, a political-risk consultancy

This appears in the May 25, 2015 issue of TIME.

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